Finite Group Databasebeta

← #49157913

Subgroups — #49157913

Order 37504.

256 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34036799C211yesmaximal, characteristic
2#34036501C211yesmaximal, characteristic, complemented
3#34036425C211yesmaximal, characteristic, complemented
4#34036420C211yesmaximal, characteristic, complemented
5#34035859C211yesmaximal, characteristic, complemented
6#34035856C211yesmaximal, characteristic, complemented
7#331×C293C211yesmaximal, characteristic, complemented
8C2×#17989801—21no—
9C2×#17989790—22no—
10#22627624C2211yescharacteristic
11#22627620—21no—
12#22627596—22no—
13#22627595—21no—
14C4×Dic586C2211yescharacteristic
15C4×D1172C2211yescharacteristic
16D4×Dic293—21no—
17#22627558—21no—
18#22627556—21no—
19#22627549—21no—
20#22627546—21no—
21C4×#14556873C2211yescharacteristic
22#127×C293C2211yescharacteristic
23C4⋊C8×C293C2211yescharacteristic
24C4⋊C8×C293C2211yescharacteristic
25#17989801—42no—
26#17989801—42no—
27C2×Dic586—21no—
28C2×Dic586D411yescharacteristic
29C2×D1172D411yescharacteristic
30C2×C22⋊D293—22no—
31C2×C22⋊D293—22no—
32C22×Dic293—22no—
33C2×C4×D293—21no—
34#17989790—44no—
35C2×#14556873—21no—
36C4⋊Dic293—21no—
37C4⋊Dic293—21no—
38C4⋊Dic293D411yescharacteristic
39C4⋊Dic293D411yescharacteristic
40#17989781—21no—
41C22⋊Dic293—22no—
42#17989779—21no—
43C4×Dic293—21no—
44C2×D4×C293—21no—
45C2×D4×C293—21no—
46C2×D4×C293D412yes—
47C2×C8×C293—21no—
48C2×C8×C293—21no—
49C42×C293C2311yescharacteristic
50C22×D293—21no—
51Dic586—21no—
52Dic586—42no—
53Dic586SD1612yescomplemented
54D1172—21no—
55D1172—21no—
56C22⋊D293—44no—
57C22⋊D293—82no—
58C2×Dic293—21no—
59C2×Dic293—21no—
60C2×Dic293—21no—
61C2×Dic293—44no—
62C2×Dic293—41no—
63C4×D293—41no—
64C4×D293—41no—
65#14556873—22no—
66C23×C293—22no—
67D4×C293—42no—
68D4×C293—41no—
69D4×C293—41no—
70D4×C293—41no—
71D4×C293—41no—
72C2×C4×C293C2×D411yescharacteristic
73C2×C4×C293C2×D411yescharacteristic
74C2×C4×C293C2×D411yescharacteristic
75C8×C293—41no—
76C8×C293—41no—
77C22×C293—42no—
78C22×C293—42no—
79C22×C293—42no—
80C22×C293#12011yescharacteristic
81C2×D293—41no—
82C2×D293—41no—
83C2×D293—41no—
84C4×C293—21no—
85C4×C293C2×SD1611yescharacteristic
86C4×C293#13511yescharacteristic
87C4×C293AGL(1,ℤ/8)11yescharacteristic
88C4×C293#13711yescharacteristic
89Dic293—22no—
90Dic293—41no—
91Dic293—41no—
92Dic293—81no—
93C2×C293—82no—
94C2×C293#45011yescharacteristic
95C2×C293#45211yescharacteristic
96C2×C293#45311yescharacteristic
97D293—81no—
98C293#163111yescharacteristic, complemented, Sylow
99#1631—2931nomaximal, Sylow
100#550—2931no—
101#492—2931no—
102#477—2931no—
103#476—2931no—
104#331D29311yescharacteristic, complemented
105Q8⋊C8—2931no—
106D4⋊C8—2931no—
107C2×#41—5861no—
108C2×SD16—5862no—
109C4⋊Q8—2931no—
110#127—5861no—
111#127C2×D29311yescharacteristic
112#121—5861no—
113#121—5862no—
114C4×Q8—2931no—
115C4×D4—2931no—
116C4×D4—5861no—
117#107—5861no—
118#106—5861no—
119C4⋊C8C2×D29311yescharacteristic
120C4⋊C8C2×D29311yescharacteristic
121#103—5861no—
122#102—5861no—
123C4×C8—2931no—
124#41—11722no—
125#41—11722no—
126C2×Q8—2931no—
127C2×Q8—5861no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—2931no—
131C2×D4—5862no—
132C2×D4—5862no—
133C2×D4D117212yes—
134C22×C4—5862no—
135C22×C4—5861no—
136SD16—11724no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—5861no—
140C4⋊C4—2931no—
141C4⋊C4—2931no—
142C4⋊C4—5861no—
143C4⋊C4—5861no—
144C4⋊C4—5861no—
145C22⋊C4—5862no—
146C22⋊C4—5861no—
147C42—5861no—
148C42C22×D29311yescharacteristic
149C23—22no—
150C23—5861no—
151Q8—2932no—
152Q8—5861no—
153Q8—11722no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—23442no—
160D4—5861no—
161D4—5861no—
162D4—11724no—
163C2×C4—5861no—
164C2×C4—5861no—
165C2×C4—5861no—
166C2×C4—11721no—
167C2×C4—11724no—
168C2×C4—11721no—
169C2×C4—11721no—
170C2×C4D4×D29311yescharacteristic
171C2×C4D4×D29311yescharacteristic
172C2×C4C2×D117211yescharacteristic
173C8—41no—
174C8—41no—
175C8—5862no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—11721no—
180C22—11721no—
181C22—11721no—
182C22#2262759411yescharacteristic
183C4—21no—
184C4—23441no—
185C4—5862no—
186C4—11721no—
187C4—11721no—
188C4SD16×D29311yescharacteristic
189C4#2262764311yescharacteristic
190C4#2262764811yescharacteristic
191C4#2262765311yescharacteristic
192C2—82no—
193C2—23441no—
194C2#3403628111yescharacteristic
195C2#3403629211yescharacteristic
196C2#3403629911yescharacteristic
subgroupG/H
centerC22#22627594
commutator, cosocleC42×C293C23
FrattiniC42C22×D293
Fitting#331×C293C2
socleC22×C293#120
prime radical#34036799C2
hypercenter#331D293
hypocenterC293#1631
LCSG ▷ C42×C293 ▷ C22×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #34036501C2semidirect
3. #34036425C2semidirect
4. #34036420C2semidirect
5. #34035859C2semidirect
6. #34035856C2semidirect
7. #331×C293C2semidirect
53. Dic586SD16semidirect
98. C293#1631semidirect
104. #331D293semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#340367992
#340365012
#340364252
#340364202
#340358592
#340358562
#331×C2932
#1631293